The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: Mathematical analysis

摘要

In Li and Wang (2019) [11], three kinds of typical Caputo-type partial differential equations are numerically studied via the local discontinuous Galerkin (LDG) finite element methods, including Caputo-type reaction-diffusion equation, Caputo-type reaction-diffusion-wave equation, and Caputo-type cable equation without regularity analysis. In this article, we study the existence, uniqueness, and regularity of the solutions to these equations. Besides, the error estimate for Caputo-type cable equation has been greatly improved.